The present invention relates to a new and distinct raspberry variety designated ‘DrisRaspEight’ and botanically known as Rubus idaeus L. This new raspberry variety was discovered in Ventura County, Calif. in October 2008 and originated from a cross between the proprietary female parent raspberry plant ‘Driscoll Estrella’ (U.S. Plant Pat. No. 19,137) and the proprietary male parent raspberry plant ‘DrisRaspFour’ (U.S. Plant Pat. No. 22,731). The original seedling of the new variety was first asexually propagated via tissue culture at a nursery in Santa Cruz County, Calif. in 2008. ‘DrisRaspEight’ was subsequently asexually propagated and underwent further testing at a nursery in Santa Cruz County, Calif. for seven years. The present invention has been found to be stable and reproduce true to type through successive asexual propagations via tissue culture and root cuttings.